We consider strongly correlated limit of variants of the Hubbard model (HM) in which on parts of the system it is energetically favourable to project out doublons from the low energy Hilbert space while on other sites of the system it is favourable to project out holes while still allowing for doublons. As an effect the low energy Hilbert space itself varies with sites of the system. Though the formalism is well developed for the case of doublon projection in the literature, case of hole projection has not been explored in detail so far. We derive basic framework by defining creation and annihilation operators for electrons in a restricted Hilbert space where holes are projected out but which still allows for doublons. We generalise the idea of Gutzwiller approximation for case of hole projection which has been done in literature for the case of doublon projection. To be specific, we provide detailed analysis of strongly correlated limit of the ionic Hubbard model (IHM) which has a staggered potential ∆ on two sublattices of a bipartite lattice and the correlated binary alloys which have binary disorder ±V /2 randomly distributed on sites of the lattice. In both the cases, for ∆ ∼ U ≫ t and for V ∼ U ≫ t, where U is the Hubbard energy cost for having a doublon at a site, there are sites on which doublons are allowed while holes are the maximum energy states. We do a systematic generalization of similarity transformation for both these cases and obtain the effective low energy Hamiltonian. We further derive Gutzwiller approximation factors which provide renormalization of various terms in the effective low energy Hamiltonian due to the Gutzwiller projection operators, excluding holes on some sites and doublons on the remaining sites.

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We introduce a disorder-free model of S=1/2S=1/2 spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums". These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.

Objective Oro-antral communication (OAC) is one of the most frequently encountered complications during third molar extraction. Various radiographic factors, like excessive maxillary sinus pneumatization, long periods of edentulism, periapical lesions, etc., have been considered high-risk factors for OAC. However, a panoramic radiograph has not proven to be accurate in predicting the chances of OAC. Through this retrospective study, we evaluated the efficacy of a CBCT in predicting the incidence of OAC after maxillary third molar extraction. Materials and Methods We conducted a retrospective study in our department, which included the patients who had undergone extraction of a maxillary third molar over five years with the presence of panoramic X-rays and/or CBCT scans prior to extraction. Primary outcomes assessed from the case files were intra-operative complications like OAC, root fracture, tuberosity fracture, pterygoid plate fracture, etc. The incidence of these complications was correlated with the presence or absence of CBCT before extraction. Results Out of 920 extracted maxillary third molar, only 148 teeth (16.1%) had a CBCT record before extraction. The most commonly encountered complication was broken inaccessible root piece/s (4.9%), followed by OAC (3.5%). An inter-group comparison showed that a significantly higher percentage of patients (p < 0.001) with CBCT records had an incidence of OAC (11.5%) as against the group of patients with no CBCT record (1.9%). Conclusion A CBCT scan prior to cases with high-risk factors for OAC can be a valuable tool in accurately predicting the chances of OAC after maxillary third molar extraction.